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Review : Going nuts over numbers

By Robert Matthews

WHY do otherwise normal people, often very successful in their own field,
devote years to finding something that can’t exist—a simple formula for
generating prime numbers or a solution to quintic equations?

In this Cook’s tour of crankery, first published by the Mathematical
Association of America in 1992, Dudley Underwood extracts insights from an
astonishing variety of examples in his Mathematical Cranks (Cambridge,
£17.95, ISBN 0 88385 507 0). With the dedication of, well, a crank, he
contacted hundreds of mathematics departments and friends asking for examples.
He was rewarded with “proofs” of everything from Fermat’s last theorem to the
trisection of angles.

One recurring theme is that cranks seem to have a problem with
authority—a real problem in mathematics. Sadly, history shows that if some
geezer called Gauss proved something impossible years ago, that’s
it—finito.

Not all cranks attempt the provably impossible, of course: some attack
problems where proof has eluded the experts, and here a bad attitude towards
authority is no bad thing. For example, there is as yet no proof that every even
integer greater than 4 is the sum of two odd primes. The problem is that
amateurs almost certainly lack the expertise to succeed where countless
professionals have failed.

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That said, it is—just—possible that there is a second Gauss out
there working in insurance who does have, say, a natty proof of the infinitude
of prime pairs. One is reminded of Niels Abel, the son of a Protestant minister,
and the Indian civil servant Srinivasa Ramanujan, two world-class mathematicians
who initially had their brilliant work dismissed as crankery. Dudley’s tediously
comprehensive study fails to acknowledge this admittedly remote possibility.

Sadly, however, most work by cranks—incomprehensible, boring and
wrong—is all too accurately reflected here.